Background of study INTRODUCTION
Mathematics is one of the subjects that occupy an important role in education. As seen from time spent in math in school, more than the other
subjects given at all levels of education starting from elementary school to college. According to Wil
liam Mathematics’ Arizona Education said that: mathematics is a human endeavor; and humanity is brought together
throught matematics”. Mathematics is essentially the activities of human life, how to live, how we are shaped by the social environment and growth
of a civilization. In the activities we would have experienced activities that involve math in it. And the activities that we will experience continued
until the future. Therefore, learning of mathematics is essential in education.
As Cornellius in Abdurrahman, 2009: 253 states that there is five reason for studying mathematics there is a means of clear and logical
thingking; a means to solve the problems in everyday; the means to know the patterns of relationships and generalization of experiences; the means
to develop creativity and a means to raise awareness of cultural development. However, a problem that often arises is inactivity students in
learning mathematics.Students follow the process learning by the teacher in the classroom by listening but do not criticism to teachers as feedback
from the process of teaching and learning.This makes students become passive and can not solve problems in mathematics and tend to memorize
concepts. These conditions make the students less interested in math. To solve the problem is needed some strategies named problem
solving. Mathematical problem solving is a process which involved the method solution is unknown in advance. To find the solution, student
should map their knowledge about mathematics. There are found important phases to solve mathematics problem. Problem solving ability
according to Polya 2004 will be measured through students’ ability to complete a problem by using problem solving steps as follows:
1. Understanding the problem
From this step, student should understand the problem that can be looked from being able to point out what the data, what the
condition, and also what the problem showed. 2.
Devising a plan From this step, students make plan how to solve the problem, which
solution that correspond to the problem. Finding the connection between the data and the unknown.
3. Carring out the plan
From this step, students implement the plan of what they have planned before.
4. Looking back
Student able to derive the result differently and use method for some other problem.
When researcher teach in PPL, researcher has make the diagnostic testin SMA N 2 Balige during follow experience teaching in school or
generally called “Program Pengalaman Lapangan Terpadu” on Agustus 22
th
until November 28
th
observations carried out in class XI IA. Number of students about 30 student per class. Diagnostic tests conducted by
researcher by giving the problem to see students’ problem solving ability. Giving diagnostic test carried out on October 12
th
2016. There are 30 students answer the diagnostic test in class XI IA 3. The problem tested to
students as follow:
Sudut-sudut segitiga ABCD adalah , �� . Jika sin = dengan
adalah sudut lancip maka tan + adalah..
From the answers given by student obtained: 1.
Students could not understand the problem
Figure 1.1 Student’s sheet in understanding the problem step
Students were able to identify what is asked but they did not able to identify whats is known. From the image above, student did not
know clearly what is known. In this step, there are 15 of 17 students could not understand the problem.
2. Students could not devise a plan in problem solving strategies
Figure 1.2 Student’s sheet in devising a plan
From this figure, students still did not make a right sketch drawing. They draw a sketch but did not make the explanation of the drawing.
From the 17 students, thay are no one make the sketch explanation. 3.
Students could not carry out the plan in problem solving strategies
Figure 1.3 Student’s sheet in carrying out the plan
From this figure, students could not do the completion based on the plan. Students could not find an appropriate strategy to solve the
problem. There are 13 of 17 could not implement problem solving strategy.
4.
Students did not look back the solution carefully and they could not derive the solution differently.
Figure 1.4 Student’s sheet in looking back the solution
Most of students did not check back their task carefully. They also could not derive the solution differently.There are no student did not
look back the solution carefully and could not derive the result differently.
Table 1.1 Table of Preliminary Diagnostic Test
Aspect Categorized
Not Categorized
High
Medium
Low 1.
Understanding the Problem
46.66 23.33
13.33
16.66 2.
Devising a plan
13.33 23.33
40.00
23.33
3. Carrying out the plan
23.33 16.66
13.33 46.66
4. Looking Back
- -
6.66
93.33
From the diagnostic test of problem solving ability above, many students still can not understand the problem, make the question into
mathematics model and formulate the problem. From this table, shown that students still have low ability in problem solving. Fourth aspects of
problem solving throught the diagnostic test, were still not reached yet as well by students, this is happen because students are not able to figure out
the problem in their mind and can not make the problem into the mathematics model and also formulate the problem.
In addition to interviews, the researchers also observed the process of learning mathematics in class XI when the learning process , researchers
found: Some students are more passive and less response to the material
being taught Students are more memorizing formulas and notes the important
things without knowing the concept Most students do not want to ask and just listening to the teacher
At the given task or problem, students can answer well through the
formulas given. However, when there is a matter that is slightly different from the examples and formula, the students immediately
apparent confusion. Recognizing the reality on the ground that the learning activity and
the problem solving ability of students is still low. We need a model of learning that make the student become active. It required a learning model
that can support successful learning. According to Ausubel Dahar, 2006 The new paradigm in education today is to create meaningful learning
process, the learning process that takes place in schools let students actively in involved in learning students-oriented. As a manager of
student learning, teacher are obliged to improved attention and efforts in providing school mathematics learning, so the lesson material can be
understood by students. Students are required to be better to use the ability of thingking to be skilled in problem solving in daily life relatedto
mathematics. Various efforts continue to be developed by the instigators of
education for the learning of mathematics in order to maximize on reaching the desired objectives, in terms of models, strategies and learning
methods in accordance with the concepts being taught. According to Berns 2011 said that one of the alternatives that can be done to overcome these
problems is to use appropriate learning models namely Contextual Teaching and Learning. This model is very supportive to improve the
activity of the students because it provides a learning contextually or involves events experienced in daily life as a person, family members, and
community members. If students know the application of learning by looking at students everyday itself, then it can be more active, problem
solving, and also further develop the lesson. Contextual Teaching and Learning is a concept of learning that
help teacher to connect between what is taught with students’ realworld situation an encorage students make connection between knowledge
possessed and its application in daily life, that involve seven main componets, they are: contructivism, questioning, inquiry, learning
community, modelling, and authentic assessment Trianto 2009. Based on the matters described above, the researcher interested in
conducting research by the title “The Application of Contextual Teaching
and Learning to Improvethe Activity and Problem Solving Ability in SMA
N 2”